【摘 要】
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We consider the convergence P sets of formal power series of the form f(z; t)= Sigma_{j=0}^infty fj(z)t^j,where fj(z)are holomorphic functions on a domain O
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We consider the convergence P sets of formal power series of the form f(z; t)= Sigma_{j=0}^infty fj(z)t^j,where fj(z)are holomorphic functions on a domain Omega in C.A subset E of Omega is said to be a convergence set in Omega if there is a series f(z; t)such that E is exactly the set of points z for which f(z; t)converges as a power series in a single variable t in some neighborhood of the origin.A sigma holomorphically-convex set in Omega is defined to be the union of a countable collection of holomorphically convex compact subsets of Omega.We prove that a subset of Omega is a convergence set if and only if it is sigma-holomorphically-convex.
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